Coupling device



July 15, 1941.

COUPLING DEVICE Filed Feb. 28', 1939 Mmmm Patented `luly l5, 1941 'r orsi COUPLING DEVICE George H. Brown, Haddonield, N. J., assigner to Radio Corporation of America, a corporation of Delaware This invention relates to coupling devices, and more particularly to means for increasing the width of the frequency characteristic of coupling transformers or the like.

The use of a quarter wave resonant line as an impedance inverter is well known. Such a line has uniformly distributed inductance and capacity. Its input impedance is inductive at frequencies on one side of resonance, capacitive at frequencies on the other side of resonance, and resistive at the resonant frequency, where the resonant frequency is that frequency at which the length of each conductor is a quarter wave. If such an inverter is connected to a modulated carrier source, it presents to the carrier source a resistive impedance, and to all side band frequencies its impedance is reactive.

It is usually desirable to keep the reactance of a crcuit constant throughout the frequency range of the applied voltage. It previously has been the custom to accomplish this to a limited extent by loading the resonant circuit with a certain amount of resistance to decrease the sharpness of the resonance curve. This method, however, introduces excessive losses in the circuit, and is not entirely satisfactory.

It is, therefore, the primary object of this invention to provide a transformer which eciently couples devices of different impedance without introducing lossesV and which presents a uniform impedance to each device over a wide range of frequencies, This invention will be better understood from the following description when considered in connection with the accompanying drawing, in which Figure 1 represents a single quarter wave resonant line; Figure 2 is the reactance curve of the resonant line ofV Fig. 1; Figure 3 is a transformer made in accordance with this invention; Figure 4 is the reactance curve of the resonant line combination of Fig'. 3; and Figure 5 is an illustration to aid in the theoretical discussion.

Referring to Fig. 1, Ro is the impedance of an output device El which is to be matched to the impedance R1 of an input device I. These iinpedances may, of course, represent the impedance of a transmission line, antenna, vacuum tube, or any other radio device. To provide proper matching, the impedance Ro must be converted to an impedance R1. While the function of the quarter wave line in this connection is'well known, it is to be understood that this invention is not limited to a quarter wave transmission line impedance inverter. The equivalent circuit which consists of a plurality of inductors and capacitors connected to form a plurality of T sections, for example, may be substituted. In addition, while the physical length of the quarter wave line will theoretically be equal to one quarter of the resonant wave length, it must be understood that the line characteristics may be influenced by inductive or capacitive loads, in which case the actual length of the line will have to be adjusted to restore the circuit to resonance.

If Zo is the characteristic impedance of the transmission line of Fig. 1, its value at the resonant frequency Zo may be expressed in the fol' lowing terms:

Zo2=RoR1 (l) Curve X of Fig. 2 illustrates the variations in the reactance of the transmission line of Fig. 1 when the frequency is varied between zero and twice the resonant frequency. Curve R represents the pure resistance component of the line between the same frequency limits.

It is to be noted that at Zero frequency the input impedance is equal to R0, and the reactance is zero. Likewise, at 210, at which frequency each conductor is one-half wave length long, the reactance is Zero and the input impedance is again equal to R0. At fo, however, while they reactance is zero, the resistance has been reduced to a value R1 which depends on the ratio of trans- Tij-3:

Referring to Fig. 3, a transformer is shown in accordance with this invention which fulfills the conditions of Equation 2 when the mid-impedance, Zm, is related to the output impedance Ro and the input impedance R1 as follows:

That is, the midimpedance is made equal to the geometric mean of the input and output impedances. To accomplish this, the dimensions of the conductors and theirrelative spacings `are adjusted until the desired relation is obtained.

By analogy to Equation 1 the equations for the characteristic impedances of the respective transmission lines of Fig. 3 Will be Z02=R0Zm and Z12=R1Zm (5) from which it follows that:

Zum/Ramon 6) and Z1 R11/RUR, 7)

The proof that a transformer consisting of a plurality of serially connected quarter Wave sections in which the midimpedance is equal to the geometric mean of the input and output impedances has a flat reactance characteristic at the resonant frequency will now be given.

Referring to Fig. 5, a general equation for the impedance ZAB looking into terminals A-B when disconnected from C-D is:

Where a is the line length, and

If then the impedance ZAB is considered as the load across the terminals C-D, then the impedance ZEF looking into terminals E-F becomes:

= ZAB cos Ka-l-j Z1 sin Ka)Z 10 ZlcosKa--jZABsinKa 1 and substituting the value of ZAB from (8) ZEF R cos Ka-i-j Zo sin Ka and when Ka=90 the denominator above reduces Z04 and the numerator reduces to 0, that is, as shown in Figs. 2 and 4, the reactance is zero at the frequency Jo at which the lines are The desired condition that the slope of the reactance curve be equal to zero at the operating wave length is satisfied when the derivative is Zero. To satisfy this condition it is necessary that mwa zo COS Z1 Sill Ia ZEF:

Z1 cos Ka-i-j Z0 sin Ka Dividing the numerator and the denominator by the term Zo cos Ka-l-iRn sin Ka, and collecting terms R0 cos Ka-l-j Z0 sin Ka Z0 cos Ka-l-j R0 sin Ka This expression is seen tobe in the form a-l-jb c-i-jd which may be rationalized Ro2Z1-Zo320 (21) thus R02Z1=Zo3 01 R04Z12=Zo6 (22) therefore Z12=Zo6/Ro4 (23) and since when Kal-:90

ZrLz

RII-R1 (24) The reactive component X may be obtained by from which it is apparent that selecting from (12) terms corresponding to bc --adV XEF:

by substituting the value of Z12 in Equation 23 we obtain R1Z02 f Z04=R1Ro3 (26) Zo2 :R01/RiBa (27) and Z0 1/ R01/R112() 28) and likewise by substituting the Value of Zoz from Equation 24 in Equation 23 there is obtained z1 Jaw/1TH; 29) It has therefore been shown that when two quarter wave resonant lines are connected in series, and when their respective characteristic impedances are related to the input and output impedances Rn and R1 in the manner shown by Equations 28 and 29, then the reactance of the transformer looking into the terminals E-F will be substantially independent of the applied irequency throughout a range on either side of the exact resonant frequency. This must be so since the slope of the reactance curve is Zero at this point.V

Fig. 4 illustrates the reactance and resistance characteristics which are obtained by the transformer shown in Fig. 3. As before, the reactance is zero at fu and 2in, while the resistance at zero and 2fo is equal to the output resistance Re. However, the resistance is low over a wider frequency range than before. As an example of the eiciency of this system, if ,fo is taken to be 90 megacycles, the reactance would be substantially a zero throughout a range extending from 60 to 120 megacycles. It is also important to note that this result has been accomplished without loss of power. The full input energy is therefore available at the output.

For a still wider response characteristic, more quarter wave sections may be added, provided their respective characteristic impedances are related to the mid-impedance by the geometric mean. Thus, if four sections are used, a similar solution which includes determining the second derivative will show that the four characteristic impedances will be where, as before R is the impedance of the source and R1 is the impedance looking into the transformer network.

In this instance, by setting the second deriva# tive equal to zero, the condition is imposed that the rate of change of the slope of the reactance curve is zero on either side of the resonant frequency.

To obtain a physical -concept of the operation of this invention, consider the efect of changing the frequency of the applied voltage so that the quarter wave lines are no longer exactly resonant. From Fig. 2 it is apparent that the input impedance immediately becomes reactive. Suppose, for example, the frequency is changed so that a given inductive impedance is present at the terminals A-B of Fig. 5. The second quarter wave line is an impedance inverter, and consequently the impedance looking into the terminals E-F now becomes capacitive. However, the second line is also oi resonance, so that it, too, adds an inductive component, which cancels a portion of the capacitive reactance. Thus the magnitude of the reactance has decreased by the action of the second serially connected quarter wave line. Additional sections increase this eiect, but for practical purposes the additional advantage is more than oiset by the additional cost, so that it is generally preferable to limit the transformer to the minimum number of sections which will provide the necessary band width.

I have thus described a coupling transformer which consists of a plurality of serially connected quarter wave sections each having a diierent characteristic impedance which, when properly related to the input and output impedances, provides a substantially flat frequency vs. reactance characteristic for frequencies on either side of the normal resonant frequency of the sections.

I claim as my invention:

1. A coupling system fortransferring energy between an output device having a terminal impedance Ro and an input devi-ce having an input impedance R1 which includes two circuits connected in series between said output and input devices, said circuits having characteristic impedances which are respectively satised by the equations:

Z1 1/ iin/Rta where Zo is the characteristic impedance of the circuit connected to the output device and Z1 is the characteristic impedance of the circuit connected to the input device.

2. A coupling system for transferring energy between an output device and an input device which includes two quarter Wave transmission lines connected in series between said devices, said transmission lines having characteristic impedances respectively satised by the equations:

and ,1

where Ru is the terminal impedance oi said output device;

R1 is the terminal impedance of said input device;

Zo is the characteristic impedance of the transmission line connected to said output device; and

Z1 is the characteristic impedance of the transmission line connected to said input device.

3. A .coupling transformer adapted to connect an output device and an input device which includes two circuits connected in series, said circuits having characteristic impedances which are of such a value that the mid-impedance is equal to the geometric mean of the output and input impedances.

4. A coupling transformer adapted to connect an output device and an input device, said transformer including a plurality of serially connected circuits, said circuits having characteristic impedances of such a value that the mid-impedance is equal to the geometric mean of the output and input impedances.

5. A coupling transformer adapted to connect an output device and an input device, said transformer comprising four -circuits connected in series, said circuits having characteristic impedances which are respectively satisied by the equations:

kvm. @Jim ,adi/m zwi/1357??? Where Zu is the characteristic impedance of the circuit to be connected to the output impedance;

Z1 and Zz are the respective characteristic impedances of intermediate circuits;

Z3 is the characteristic impedance of the circuit to be connected to the input impedance;

Ro is the output impedance; and

R1 is the input impedance.

comprising n serially connected quarter Wave matching sections whose respective characteristic impedances are chosen so that the midimpedance of said transformer is equal to the geometric mean of the impedances of the input and output devices, and in which the characteristic impedance of any section is equal to the geometric mean of the impedances of the adjacent sections, where 1l. is any even number.

8. A transformer for coupling a first device and a second device, the impedances of said devices being matched over a Wide band of frequencies, said transformer comprising n serially connected quarter Wave sections, the characteristic impedance Zm of any section being equal to Where Ro is the impedance of said rst device, R1 is the impedance of said second device, m is the number of the section Zm, counted from the rst device, and n is any even number.

GEORGE H. BROWN. 

